Correlations of the density and of the current in non-equilibrium diffusive systems

TL;DR

This paper employs fluctuating hydrodynamics to analyze density and current correlations in non-equilibrium diffusive systems, deriving general relations and validating them against exact solutions of the symmetric exclusion process.

Contribution

It derives two-time correlations of density and current in non-equilibrium steady states using hydrodynamics and generalizes the fluctuation dissipation relation.

Findings

Derived explicit formulas for correlations in non-equilibrium steady states

Validated hydrodynamic predictions with exact solutions of the symmetric exclusion process

Extended fluctuation dissipation relations to non-equilibrium conditions

Abstract

We use fluctuating hydrodynamics to analyze the dynamical properties in the non-equilibrium steady state of a diffusive system coupled with reservoirs. We derive the two-time correlations of the density and of the current in the hydrodynamic limit in terms of the diffusivity and the mobility. Within this hydrodynamic framework we discuss a generalization of the fluctuation dissipation relation in a non-equilibrium steady state where the response function is expressed in terms of the two-time correlations. We compare our results to an exact solution of the symmetric exclusion process. This exact solution also allows one to directly verify the fluctuating hydrodynamics equation.